Evaluate
21
Factor
3\times 7
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\begin{array}{l}\phantom{13)}\phantom{1}\\13\overline{)273}\\\end{array}
Use the 1^{st} digit 2 from dividend 273
\begin{array}{l}\phantom{13)}0\phantom{2}\\13\overline{)273}\\\end{array}
Since 2 is less than 13, use the next digit 7 from dividend 273 and add 0 to the quotient
\begin{array}{l}\phantom{13)}0\phantom{3}\\13\overline{)273}\\\end{array}
Use the 2^{nd} digit 7 from dividend 273
\begin{array}{l}\phantom{13)}02\phantom{4}\\13\overline{)273}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}1\\\end{array}
Find closest multiple of 13 to 27. We see that 2 \times 13 = 26 is the nearest. Now subtract 26 from 27 to get reminder 1. Add 2 to quotient.
\begin{array}{l}\phantom{13)}02\phantom{5}\\13\overline{)273}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}13\\\end{array}
Use the 3^{rd} digit 3 from dividend 273
\begin{array}{l}\phantom{13)}021\phantom{6}\\13\overline{)273}\\\phantom{13)}\underline{\phantom{}26\phantom{9}}\\\phantom{13)9}13\\\phantom{13)}\underline{\phantom{9}13\phantom{}}\\\phantom{13)999}0\\\end{array}
Find closest multiple of 13 to 13. We see that 1 \times 13 = 13 is the nearest. Now subtract 13 from 13 to get reminder 0. Add 1 to quotient.
\text{Quotient: }21 \text{Reminder: }0
Since 0 is less than 13, stop the division. The reminder is 0. The topmost line 021 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 21.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}